Some complex differential equations arising in telecommunications

Abstract

The control equations describing the removal of distortion from a transmitted digital signal are complex nonlinear coupled ordinary differential equations in real time. The simplest of the class of such equations is studied for its bifurcation structure, by a combination of analytical and numerical techniques. We find that Hopf bifurcations are possible, but the limit cycles exist only at bifurcation. Actual data is used in numerical integrations. When parameters are chosen which are appropriate to the telecommunications context, all fixed points are stable and no Hopf bifurcations occur.